To prove if your Work be true, Cube the Root, and to that Cube add the Remainder, and that Sum will be the fame as the Number given to be extracted. But if the mixt Number or Fraction be commenfurable to its Root, then extract the Cube Root of the Numerator for the Numerator of the Root, and the Cube Root of the Denominator for the Denominator of the Root; fo the Cube Root of will be, for the Cube Root of 8 is 2, and of 27 3; which is and fo of 433 and fo of any other. is Questions Questions to exercise the Cube Root. F a Bullet, whofe Diameter is 4 Inches, weigh 9 Pound, what will a Bullet of the fame Metal weigh, whofe Diameter is 8 Inches? IF a whole is R U L E. Like Solids are in triple Proportion to their homologous Sides, Diameters, Lines, &c. ; it will be as the Cube of the Diameter is to its given Weight, fo is the Cube of the other Diameter to the Weight fought. C.D. b. :: C.D.: Ib. If 64 64=72 lb. 9 512 72. For 512X9=4608÷ If the Diameter of a Globe be 1 Inch, and the Solidity thereof be ,5238 of an Inch; what is the Solidity of another Globe, whofe Diameter is 10 Inches? C.D.: S. :: C.D. : S. If 1,5238 :: 1000: 523,8 Inches. For ,5238×1000=523,8009÷1=523,8 the Solidity. If a Globe of Silver of 1 Inch Diameter, be worth 14,4 Shillings, what will another Globe of Silver be worth, whofe Diameter is 4 Inches? : If 1 : 14,4 :: 6+ 921,6. For 14,4×64= 921,61 921,6 Shillings, that is 461. is. 7d. If a Saker of 3,75 Inches Diameter at the Bore, require 4lb. of Powder for its Charge; what will a Demi-Canon of 6,5 Inches in the Bore, require for its Charge? C. D. If 52,734375 lb. C. D. 4:: 274,625: 20,83. For 274,025 X 4 = 1098,500 ÷ 52,734375= 20,83 lb. the Answer. If a Brafs Saker, whofe Diameter is 11,5 Inches, do weigh 1000 lb. what will another Piece of Ordinance (of ths fame Metal and Shape) weigh, whose Diameter is 8,75 Inches? C. D. : lb. :: C. D. lb. If 1520,875 1000 :: 669,921875: 440,484 If a Ship, whofe Burthen is 300 Tun, be 75 Feet in the Keel, what fhall be the Burthen of another Ship (of the the fame Mold) whofe Keel is 100 Feet? C. K. : Tun :: C. K. If 421875 Tun. 1000000 : 711,111. If a Bullet, whofe Diameter is 4 Inches, weigh 9 Ib. what is the Diameter of another Bullet (of the fame Metal) whofe Weight is 72 lb.? Answer 8 Inches. For, lb.: C.D. b. C.D. If 9 64 72 8 Inches the Diameter. 512; whofe Cube Root is If the Diameter of a Globe be 1 Inch, and the Solidity,5238 of an Inch, what is the Diameter of another Globe, whofe Solidity is 523,8 Inches? Anfwer, 10 Inches. For, Solid C. D.:: Solid : C.D. If,5238: I :: 523,8: 1000; whofe Cube Root is 10 Inches. I If a Globe of Silver of 1 Inch Diameter be worth 14,4 Shillings, what will be the Diameter of another. Globe of Silver that is worth 921,6 Shillings. Anfwer, 4 Inches. For, S. C.D. S. C.D. If 14,4 : I :: 921,6: 64; whofe Cube Root is 4. If you would have the Side of a Cube in Solidity to any given Solid, as Globe, Cylinder, Prism, Cone, &c the Cube Root of the Solid Content will be the Side. But if you would have the Side double, treble in Quantity, x the Solidity by 2, 3, &c. if lefs, divide by 2, 4, &c. and the Cube Root of the Product or Quotient is the Answer. Between 2 Numbers given, to find 2 mean Proportionals. Rule, x the lefs Extream by the Cube Root of the Quotient of the greater by the lefs; the Product is the leffer of the 2 mean Proportionals, which by the faid Cube Root, gives the greater Mean fought. |